Looking for Mary Mckenna Scotland

Trying to find records on Mary McKenna born about 1855 Glasgow Scotland to parents Alexander McKenna and Mary Anne Copeland. The earliest records I have on her is a Marriage in Australia to a John Turner in May 1876. She later married a George Bourne in May 1878 and also states born Glasgow Scotland.
Have not been able to find any immigration records of her arrival to Australia.

Jen